Empty Inertia

[ArturR 17]

Hi all. I have question regarding empty inertia parameters in aircraft data file.

I know that there are formulas:

 

Lx=(W/g)*(Rx*b/2)^2

Ly=(W/g)*(Ry*d/2)^2

Lz=(W/g)*(Rz*e/2)^2

 

Where:

W - weight (must be in kilograms?)

g - gravity (9,8?)

Rx; Ry; Rz - ??? I dont know what is it...

b - span (in meters?)

d - length (in meters?)

e - (b+d)/2 (is it correctly?)

 

Are these formulas correctly?

[+NeverEnough 78]

I just went through pulling together this info from the Thirdwire Forums:

 

In the Knowledge Base there is a formula discussed to figure moments of inertia.

 

 

Inertia (X Direction) Ix= (W/g)*(Rx*b/2)^2

Inertia (Y Direction) Iy= (W/g)*(Ry*d/2)^2

Inertia (Z Direction) Iz= (W/g)*(Rz*e/2)^2

 

where g=32.2 (gravity acceleration)

W=gross takeoff weight (lb)

b=span (ft)

d=length (ft)

e=(b+d)/2 and Rx, Ry and Rz are chosen from the following table for the aircraft type.

 

* = Multiplication

^ = Power of

/ = Division

 

Aircraft Type ROLL Rx PITCH Ry YAW Rz

Jet Fighter .266 .346 .400

 

EmptyMass=

Mass of the aircraft in kgs

 

EmptyInertia=

Inertia of the aircraft in the Y (left/right), X (Fore/aft) and Z (up/down) directions (see below for calculations)

 

ReferenceArea=

Wing area in sq. metres

 

ReferenceSpan=

Wing span in metres

 

 

All our numbers are in SI unit, so you'll need to convert from lb to kg, ft to meters, etc.

 

Empty weight is empty weight, ie, weight of aircraft itself, not the gross weight. Generally, gross weight means aircraft at take-off - with fuel, ammo, weapons, pilots, oil, and any other equipments. etc. You need to specify the empty weight in data file, since the game will add all those extra weights of consumables on top of it at run time.

 

The formula for moments of inertia is "correct", but you need to understand that the values of Rx, Ry, Rz you have are based on statistical figures. In reality, every aircraft will have different Rx, Ry, Rz. But since they are difficult to obtain at aircraft design stage, people use "average" of past aircraft to estimate what they would be. So unless your aircraft matches mass distribution of "average jet fighters" that they used to obtain your set of values, it will not give you exact values. The set of Rx,Ry,Rz values I used are different from what you have, for example, they are from different book which sampled different set of past aircraft...

 

If you're looking to put exact moment-of-inertia values for aircraft, you generally want to skip Rx,y,z and get Ix,y,z directly instead. These data can be difficult to come by, but they are sometimes published in reports and books with other aerodynamic coefficients. You can try NACA report server, or look though some aero design books (which might have tables of some historical airplane data), etc. Generally you won't get empty Ix,Iy,Iz, so you'll need to find the weight they were measured at, and scale them down to empty weight.

 

Having said that, .266 .346 .400 should give you good estimate for F-86 (F-86 being fairly "average" jet fighter in its configuration).

 

The only thing I'd double check, make sure the axis are in the right order. Our game's x-axis is left-right, y-axis nose-tail, so EmptyInertia= should list I-pitch, I-roll, I-yaw, in that in the order. You should generally end up with the smallest moment inertia in the second value (roll).

TK

[ArturR 17]

Thanks NeverEnough for this info.

So using as an example WoE stock F-15A data

We have:

 

[AircraftData]

EmptyMass=12474.0

EmptyInertia=260995.5,31548.9,286808.2

ReferenceArea=56.49

ReferenceSpan=13.01

ReferenceChord=4.86

CGPosition=0.0,0.20,0.0

 

Where

I-pitch=260995.5

I-roll=31548.9

I-yaw=286808.2

 

d=19.43 (length)

b=13.01 (span)

e=(b+d)/2

 

Inertia (Y Direction) Iy= (W/g)*(Ry*d/2)^2

(12474/9.8) * (Ry*19.43/2)^2 = 260995.5

1272.86 * 94.38Ry = 260995.5

120131.53Ry = 260995.5

Ry = 2.173

 

Inertia (X Direction) Ix= (W/g)*(Rx*b/2)^2

1272.86 * (Rx*13.01/2)^2 = 31548.9

Rx = 0.586

 

Inertia (Z Direction) Iz= (W/g)*(Rz*e/2)^2

1272.86 * (Rz*16.22/2)^2 = 286808.2

Rz = 3.426

 

Is that correct?

Edited September 22, 2009 by ArturR

[Tzareff 6]

yep it seems corect but i still dont know how you manage to calculate Rx ;Ry ; Rz for F-15. My mathematic skills are pathetic sory i will try to understand it but my calculator says that TK use diferent Rx ,Ry,Rz for the diferent planes  thank you.